We present the Three-mm Ultimate Mopra Milky Way Survey, a new mm-wave molecular-line mapping survey of the southern Galactic Plane, and its first data releases and science results. ThrUMMS maps a 60° × 2° sector of our Galaxy's fourth quadrant, using a combination of fast mapping techniques with the Mopra radio telescope, simultaneously in the J = 1→0 lines of 12CO, 13CO, C18O, and CN near 112 GHz, at 1′.2 and 0.3 km s−1 resolution, with 1.2 K/ch sensitivity for 12CO and 0.7 K/ch for the other transitions. The calibrated data cubes from these observations are made freely available to the community on the ThrUMMS website, http://www.astro.ufl.edu/thrumms, after processing through our pipeline. Here, we summarise the first science results, on global variations in the iso-CO line ratios and on a detailed multiwavelength study of the GMCs near l=333°.